Gearing



J. O. ALMEN Aug. 31, 1954 GEARING Filed July 14, 1949 Patented Aug. 31,1954 r 2,687,653

I UNITED STATES PATENT OFFICE GEARING John 0. Almen, Royal Oak, Mich.,assignor to General Motors Corporation, Detroit, Mich., a corporation ofDelaware Application July 14, 1949, Serial No. 104,721

10 Claims. (Cl. 74417) to obtain substantially uniform distribution ofthe maximum load.

the load acting on the gear teeth over the entire Another object of theinvention is to provide face width of the gear. an improved gear disc orwheel with the ele- The present practice in gear design appears to mentslocated in substantial alignment with the be to form the gears and theirsupporting struccomponent ofthe resultant tooth load at the tural partssufficiently massive to hold the teeth point of contact for gears havingteeth angularly rigid or without deflection when load is applied relatedto the axis of the gear. to the teeth. This is necessary since the gearAnother object of the invention is to provide and the supportingstructural parts is eccentric contact and in the plane of the axes ofthe meshbe accomplished if the gear web and rim of a gear" tion circleof the gear teeth and having the rethat they will deflect in thedirection to uniallel to the elements of the conical disc.

formly distribute the load across the width of These and other objectsof the invention will the teeth, and the gear web is made in substanbeapparent from the following description and tial alignment to theresultant of the tooth load drawings.

passing through the shaft axis, so that the thin In the drawings, Figure1 is a meshing pair of gear web will support the tooth load. In spurspiral bevel gears.

gearing a thin radial web is employed which is Figure 2 is an isometricview of the spiral bevel joined to the rim at its center. The thin webgears showing the tooth load forces.

or disc deflects to allow angular or radial move- The invention isillustrated in connection with helical, spiral, bevel, spiral bevel orhypoid gears, disc is flexible to obtain substantially uniform Tocontrol this deflection or to allow the use of The driving pinion I0 isformed integrally with through the axis of the gear. In order to correctand meshes with driven gear rim and teeth 20, for deflection loads thediameter at which the which rotates about its axis 22 located at rightdisc is joined to the bevel or spiral bevel gear angles to andintersecting axis 18. The gear should be smaller than the theoreticaldiameter rim 20 is supported by a conical disc 24 suitably improved gearweb which is sufficiently flexible the bearings are supported by asuitable housing right angles. to-each .other are the. complete force.

- vectors are drawn 1 the axis. of the gears ments of the bevel gear thedirection of the resultant force 40 in the plane of the gear and pinionaxes or the resultant passing through the gear axis must be determined.The isometric view showing the gears, the axes and the cone angle, andforce vectors is shown in Figure 2. The axis l8 of the driving pinionand the axis 22 of the driven gear meet atright-angles. .Thepitch coneline 3 1 is in theplane of the axes l8 and 22 and passes through thedesign point of contact 42 on the gear teeth, angle whose tangent is thegear ratio of the pinion to the gear.

The vectors act through thepoi nt of contact 42 on the pitch cone thesake of clarity so that the vectorsdonotaoverlaythegears, the vectordiagram has through the displaced, contact point -42. As-

Figure 2 is an isometric view 18 and. .22 which are at illustrated atanangle to each other to producethe perspective effect. The force diagramwhich is; a right parallelepiped was illustrated in this-viewto showdiagram in a single view. Thus it will be seen that adjacent faces. ofthe force diagram parallelepiped are at right angles to each other. Itis also pointed outthat each face. oiuthe parallelepiped maybeconsidered a force: diagram or. parallelogram. having. a. rightparallelogram f orrn.

The vector l -l which represents. the torque force and is equal to thetorque divided by the radius of point 2 about axis i8 is drawn frompointllZ' perpendicular to the planeof the axes i8 and 22'; Since thepinion is movin clockwise as indicatedby the arrow in Figure 2, theforce above the plane of the axes. In the plane of vector M and a vector66' is drawn perpendicular to the tooth surface. at the. contact point42. The. angle S between vectors M. and lt is. the spiral angle. Theforce-parallelogram formed by the .vectors M and dd has .a. base 34"which is cone line 34 displaced for clarity. The other end or top of theforce parallelogram is parallel to the line 35. The vector A8 whichrepresents the resultant toothv load is drawn ina plane through vectorof vectors. .t' lzand ME, and. makes an angle P equal to. the toothpressure angle with vector Q6. The vector this then projected into theplane of to give vector 40.", the, resultant'horizontal tooth load. Thevector fiil is shown in the. displaced position relativeto displacedcontact point 42. The tooth load pointed out above and. .thusthe'ugearaxes vector til is showniin the proper relative-position'to the gears inFigure 2. The radial ele- -disc 2 are made in substantialalig-nment'with the vector of the resultant horizontal'tooth load.In'order to simplify the above description, the disc or web 25 has beenconsidered to be a plane or to have no thickness so that the elemet orgeneratrix would-bea straight line. Though the element or generatrixwould technically be a plane when the. thickness of thediscisconsidered, the central element or median of this. generatrix plane; isnormally and in this case referred to: asthe element of the disc. Thusthe disc fill. for thebgear is subject to a minimum bending forcev andwi'llhave a minimum deflection. It is also pointed out that the strengthof bevel gear teeth isless attheir For this" small ends thanat theirlarge ends;

pitch cone line. (i l merely the and makes an angle with the pinion axisequalto half the pitch cone angle, oran,

46 and perpendicular to. the plane 65 the disc is positioned I rim atthe center of reason the distribution of the load on bevel gears shouldnot be about the geometric mid-point but about the mid-point of thetooth in relation to its beam strength.

Tests of a conical disc indicated that the deflection of a point insidethe projected conical surface is very much greater than that of a pointoutside the projected. surface forthe same tangential load applied tothe. end of a tooth. From these relative deflections it became apparentthat for a tangential load applied on the conical surface, a linerepresenting the flank of a tooth would be tilted at an angle to themating tooth, causing-the contact to shift toward the heel of the;tooth. orthe end having the larger diameter. Byapplying the load at apoint outside the projected cone. surface, the moment caused by thisdisplacement of the load will be in such direction as to compensate forthis deflection. The conical disc 24 may be connected to the rim 20tocreate a momentltending to shift. the contact point. of the samevalue. as the moment caused by;- the. tooth load, so that they balanceto maintain the load atthe centerof the tooth, so .that the deflectionof the tooth will beparallel to itself. Thusas shown in Figure 1 theconical web 24 is connected to the rim- 2% at a point inside thetheoretical point of contact Maud the resultant lflwhich passes throughthe gear axis 13. The theoreticalpoi-nt of contact at the center of thetooth is also the point of origin for the vectors indicating. the loadson the tooth. In general the elements of the conical disc 2d areconnected to the gear rim-28 midway between the theoretical point: ofcontact at the center and the toe-or smaller diameter end of the teeth,and are connected to the-shaft at the point where the resultant vectorit intersects the shaft 26 or axis 2-2, and thus the mean element ofthe. disc and the resultant vector 43 are substantially in alignment andparallel.

It will be seen that this invention can also be applied toother typesdirected loads. Thus in spiral or helical spur gears the gear web shouldhave a similar conical shape with the elements ofthe cone in substantialalignment with the resultant force onthe gear web directed toward theaxis of the gear. In the normal helical spurgears with parallel shafts.the resultantof the separating force, the tangentialforce and thethrust, force is in the planeof these shafts. These forces arecalculated byeither trigonometry or by vector analysis. The latter typeof solution for helical gears is similar to the vector solution forspiral bevel gears shown in the above specification and drawings exceptthat thehelical gears have no cone angle. In plain bevel gears theelements. of theweb may also: bein substantial alignment with the re-The resultant is determined in the same manner as for-the spiral bevelgears, but the vectoris not tilte'd' for the spiral angle since theteeth contact will be on the pitch cone line M. In spur gears radiallyand meets the gear the teeth. The disc has a thin section so that thedisc may bend to'allow the. teeth to displace to relieve concentrationsof tooth pressure forces and to evenly distribute these forces-over theentire width of the teeth.

The above describedlspecificembodiment illus trates the principles ofthe invention Numerous applications may be-made; within the scope of theappended claimsof gears with angularly pinion, the axes of said gear andpinion defining and said elements passing through said teeth at a plane,and the web of said gear having elements a smaller diameter than saidvector.

e located substantially coincident to the resultant 9. In a gear havinggear teeth and a conical tooth load vector in the plane of said axes.Web, said teeth being at a cone angle and at a n a gear assembly, a gearhaving gear teeth pitc angle to said gear axis, said web being in and aweb, said gear teeth being unidirectional substantial alignment with theresultant tooth to the resultant tooth load vector in the plane of theface of said teeth.

gear assembly, a first gear having gear ar assembly, a first bevel gearhaving teeth and a conical web, a second gear meshing a l l y p nedteeth on the im, Said We having a thickness substantially less than thej n t h im f s d fir t r at adiamete said gear teeth displaced towardthe first gear C ta t DO cation on the teeth a distance providing amoment 5. In a gear having teeth and a web, said gear t mne th 8 teethbelng unidirectional spiral gear teeth, said placement of the point ofload application on the gear meshing with a pinion, the axes of said geateeth due to the deflection of the conical web.

having elements located substantially coincident References Cited in thefile of this patent UNITED STATES PATENTS said resultant tooth loadvector at the teeth. Number Name Date 6. In a gear having gear teeth anda web, said 1,323,232 7011 2, 1919 gear teeth being spiral bevel gearteeth, said gear I 1,900,452 Ledeen Man 1933 meshing with a pinion, theaxes of said gear and 9 5 Banyan M 6, 1934 pinion defining a plane, theweb of said gear 2,002,310 chllstman M 21, 1935 having elements locatedsubstantially coincident 50 2,516,077 Schmltter July 1950 to theresultant tooth load vector in the plane of FOREIGN PATENTS said axes,and said element passing Within said resultant tooth load vector at thetooth. Number Country Date 7, In a, ear assembly, a first gear havinggear 884461 France 1943 8 In a g elements in substantial alignment withsaid re- 10 directional angularly positioned gear teeth and a

